Supersymmetric Rényi entropy and defect operators

Abstract

We describe the defect operator interpretation of the supersymmetric Rényi entropies of superconformal field theories in three, four and five dimensions. The operators involved are supersymmetric codimension-two defects in an auxiliary ℤn gauge theory coupled to n copies of the SCFT. We compute the exact expectation values of such operators using localization, and compare the results to the supersymmetric Rényi entropy. The agreement between the two implies a relationship between the partition function on a squashed sphere and the one on a round sphere in the presence of defects.